Algebra Examples

$1 - \frac{2 u - 3}{4} = \frac{2 - 5 u}{3} - 3 u$

Step 1

Since $u$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{2 - 5 u}{3} - 3 u = 1 - \frac{2 u - 3}{4}$

Step 2

Simplify $\frac{2 - 5 u}{3} - 3 u$ .

Tap for more steps...

Step 2.1

To write $- 3 u$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 - 5 u}{3} - 3 u \cdot \frac{3}{3} = 1 - \frac{2 u - 3}{4}$

Step 2.2

Simplify terms.

Tap for more steps...

Step 2.2.1

Combine $- 3 u$ and $\frac{3}{3}$ .

$\frac{2 - 5 u}{3} + \frac{- 3 u \cdot 3}{3} = 1 - \frac{2 u - 3}{4}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{2 - 5 u - 3 u \cdot 3}{3} = 1 - \frac{2 u - 3}{4}$

Step 2.3

Simplify the numerator.

Tap for more steps...

Step 2.3.1

Multiply $3$ by $- 3$ .

$\frac{2 - 5 u - 9 u}{3} = 1 - \frac{2 u - 3}{4}$

Step 2.3.2

Subtract $9 u$ from $- 5 u$ .

$\frac{2 - 14 u}{3} = 1 - \frac{2 u - 3}{4}$

Step 2.3.3

Factor $2$ out of $2 - 14 u$ .

Tap for more steps...

Step 2.3.3.1

Factor $2$ out of $2$ .

$\frac{2 (1) - 14 u}{3} = 1 - \frac{2 u - 3}{4}$

Step 2.3.3.2

Factor $2$ out of $- 14 u$ .

$\frac{2 (1) + 2 (- 7 u)}{3} = 1 - \frac{2 u - 3}{4}$

Step 2.3.3.3

Factor $2$ out of $2 (1) + 2 (- 7 u)$ .

$\frac{2 (1 - 7 u)}{3} = 1 - \frac{2 u - 3}{4}$

Step 3

Simplify $1 - \frac{2 u - 3}{4}$ .

Tap for more steps...

Step 3.1

Combine into one fraction.

Tap for more steps...

Step 3.1.1

Write $1$ as a fraction with a common denominator.

$\frac{2 (1 - 7 u)}{3} = \frac{4}{4} - \frac{2 u - 3}{4}$

Step 3.1.2

Combine the numerators over the common denominator.

$\frac{2 (1 - 7 u)}{3} = \frac{4 - (2 u - 3)}{4}$

Step 3.2

Simplify the numerator.

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$\frac{2 (1 - 7 u)}{3} = \frac{4 - (2 u) - - 3}{4}$

Step 3.2.2

Multiply $2$ by $- 1$ .

$\frac{2 (1 - 7 u)}{3} = \frac{4 - 2 u - - 3}{4}$

Step 3.2.3

Multiply $- 1$ by $- 3$ .

$\frac{2 (1 - 7 u)}{3} = \frac{4 - 2 u + 3}{4}$

Step 3.2.4

Add $4$ and $3$ .

$\frac{2 (1 - 7 u)}{3} = \frac{- 2 u + 7}{4}$

Step 3.3

Simplify with factoring out.

Tap for more steps...

Step 3.3.1

Factor $- 1$ out of $- 2 u$ .

$\frac{2 (1 - 7 u)}{3} = \frac{- (2 u) + 7}{4}$

Step 3.3.2

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{2 (1 - 7 u)}{3} = \frac{- (2 u) - 1 (- 7)}{4}$

Step 3.3.3

Factor $- 1$ out of $- (2 u) - 1 (- 7)$ .

$\frac{2 (1 - 7 u)}{3} = \frac{- (2 u - 7)}{4}$

Step 3.3.4

Simplify the expression.

Tap for more steps...

Step 3.3.4.1

Rewrite $- (2 u - 7)$ as $- 1 (2 u - 7)$ .

$\frac{2 (1 - 7 u)}{3} = \frac{- 1 (2 u - 7)}{4}$

Step 3.3.4.2

Move the negative in front of the fraction.

$\frac{2 (1 - 7 u)}{3} = - \frac{2 u - 7}{4}$

Step 4

Move all terms containing $u$ to the left side of the equation.

Tap for more steps...

Step 4.1

Add $\frac{2 u - 7}{4}$ to both sides of the equation.

$\frac{2 (1 - 7 u)}{3} + \frac{2 u - 7}{4} = 0$

Step 4.2

To write $\frac{2 (1 - 7 u)}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 (1 - 7 u)}{3} \cdot \frac{4}{4} + \frac{2 u - 7}{4} = 0$

Step 4.3

To write $\frac{2 u - 7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 (1 - 7 u)}{3} \cdot \frac{4}{4} + \frac{2 u - 7}{4} \cdot \frac{3}{3} = 0$

Step 4.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.4.1

Multiply $\frac{2 (1 - 7 u)}{3}$ by $\frac{4}{4}$ .

$\frac{2 (1 - 7 u) \cdot 4}{3 \cdot 4} + \frac{2 u - 7}{4} \cdot \frac{3}{3} = 0$

Step 4.4.2

Multiply $3$ by $4$ .

$\frac{2 (1 - 7 u) \cdot 4}{12} + \frac{2 u - 7}{4} \cdot \frac{3}{3} = 0$

Step 4.4.3

Multiply $\frac{2 u - 7}{4}$ by $\frac{3}{3}$ .

$\frac{2 (1 - 7 u) \cdot 4}{12} + \frac{(2 u - 7) \cdot 3}{4 \cdot 3} = 0$

Step 4.4.4

Multiply $4$ by $3$ .

$\frac{2 (1 - 7 u) \cdot 4}{12} + \frac{(2 u - 7) \cdot 3}{12} = 0$

Step 4.5

Combine the numerators over the common denominator.

$\frac{2 (1 - 7 u) \cdot 4 + (2 u - 7) \cdot 3}{12} = 0$

Step 4.6

Simplify the numerator.

Tap for more steps...

Step 4.6.1

Apply the distributive property.

$\frac{(2 \cdot 1 + 2 (- 7 u)) \cdot 4 + (2 u - 7) \cdot 3}{12} = 0$

Step 4.6.2

Multiply $2$ by $1$ .

$\frac{(2 + 2 (- 7 u)) \cdot 4 + (2 u - 7) \cdot 3}{12} = 0$

Step 4.6.3

Multiply $- 7$ by $2$ .

$\frac{(2 - 14 u) \cdot 4 + (2 u - 7) \cdot 3}{12} = 0$

Step 4.6.4

Apply the distributive property.

$\frac{2 \cdot 4 - 14 u \cdot 4 + (2 u - 7) \cdot 3}{12} = 0$

Step 4.6.5

Multiply $2$ by $4$ .

$\frac{8 - 14 u \cdot 4 + (2 u - 7) \cdot 3}{12} = 0$

Step 4.6.6

Multiply $4$ by $- 14$ .

$\frac{8 - 56 u + (2 u - 7) \cdot 3}{12} = 0$

Step 4.6.7

Apply the distributive property.

$\frac{8 - 56 u + 2 u \cdot 3 - 7 \cdot 3}{12} = 0$

Step 4.6.8

Multiply $3$ by $2$ .

$\frac{8 - 56 u + 6 u - 7 \cdot 3}{12} = 0$

Step 4.6.9

Multiply $- 7$ by $3$ .

$\frac{8 - 56 u + 6 u - 21}{12} = 0$

Step 4.6.10

Subtract $21$ from $8$ .

$\frac{- 56 u + 6 u - 13}{12} = 0$

Step 4.6.11

Add $- 56 u$ and $6 u$ .

$\frac{- 50 u - 13}{12} = 0$

Step 4.7

Factor $- 1$ out of $- 50 u$ .

$\frac{- (50 u) - 13}{12} = 0$

Step 4.8

Rewrite $- 13$ as $- 1 (13)$ .

$\frac{- (50 u) - 1 (13)}{12} = 0$

Step 4.9

Factor $- 1$ out of $- (50 u) - 1 (13)$ .

$\frac{- (50 u + 13)}{12} = 0$

Step 4.10

Rewrite $- (50 u + 13)$ as $- 1 (50 u + 13)$ .

$\frac{- 1 (50 u + 13)}{12} = 0$

Step 4.11

Move the negative in front of the fraction.

$- \frac{50 u + 13}{12} = 0$

Step 5

Set the numerator equal to zero.

$50 u + 13 = 0$

Step 6

Solve the equation for $u$ .

Tap for more steps...

Step 6.1

Subtract $13$ from both sides of the equation.

$50 u = - 13$

Step 6.2

Divide each term in $50 u = - 13$ by $50$ and simplify.

Tap for more steps...

Step 6.2.1

Divide each term in $50 u = - 13$ by $50$ .

$\frac{50 u}{50} = \frac{- 13}{50}$

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

Cancel the common factor of $50$ .

Tap for more steps...

Step 6.2.2.1.1

Cancel the common factor.

$\frac{50 u}{50} = \frac{- 13}{50}$

Step 6.2.2.1.2

Divide $u$ by $1$ .

$u = \frac{- 13}{50}$

Step 6.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.3.1

Move the negative in front of the fraction.

$u = - \frac{13}{50}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$u = - \frac{13}{50}$

Decimal Form:

$u = - 0.26$